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5. Prove Corollary 3.6: "Let u and v be vertices of a 2-connected graph G. Then there is a cycle of G that contains both u and v.” (Hint: you may use Theorem 3.5.)

5. Prove Corollary 3.6: "Let u and v be vertices of a 2-connected graph G. Then there is a cycle of G that contains both u and v.” (Hint: you may use Theorem 3.5.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 21E
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Theorem 3.5 states the following: 

Let G be a loopless graph with at least three vertices, and no isolated vertices. Then G is 2-connected if and only if, for every pair {e, f} of edges of G, there is a cycle of G that contains both e and f.

5. Prove Corollary 3.6: "Let u and v be vertices of a 2-connected graph G. Then there is a cycle of G that contains both u and v.” (Hint: you may use Theorem 3.5.)
Transcribed Image Text:5. Prove Corollary 3.6: "Let u and v be vertices of a 2-connected graph G. Then there is a cycle of G that contains both u and v.” (Hint: you may use Theorem 3.5.)
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